Deck 12: Simple Regression Analysis and Correlation

Question 1

In simple regression analysis the error terms are assumed to be independent and normally distributed with zero mean and constant variance.

Answer 1

True

Question 2

In regression,the variable that is being predicted is usually referred to as the independent variable.

Answer 2

False

Question 3

Calculate confidence intervals to estimate the conditional mean of the dependent variable and prediction intervals to estimate a single value of the dependent variable.

Answer 3

One of the most prevalent uses of a regression model is to predict the values of y for given values of x.Recognizing that the predicted value is often not the same as the actual value,a confidence interval has been developed to yield a range within which the mean y value for a given x should fall.A prediction interval for a single y value for a given x value is also specified.This second interval is wider because it allows for the wide diversity of individual values,whereas the confidence interval for the mean y value reflects only the range of average y values for a given x.

Question 4

In regression,the predictor variable is called the dependent variable.

Question 5

Calculate the standard error of the estimate using the sum of squares of error,and use the standard error of the estimate to determine the fit of the model.

Question 6

One of the assumptions of simple regression analysis is that the error terms are exponentially distributed.

Question 7

The slope of the regression line,y = 21 − 5x,is 21.

Question 8

Calculate the slope and y intercept of the least squares equation of a regression line and from those,determine the equation of the regression line.

Question 9

Data points that lie apart from the rest of the points are called deviants.

Question 10

Calculate the Pearson product-moment correlation coefficient to determine if there is a correlation between two variables.

Question 11

For the regression line,y = 21 − 5x,21 is the y intercept of the line.

Question 12

Calculate the residuals of a regression line and from those determine the fit of the model,locate outliers,and test the assumptions of the regression model.

Question 13

The process of constructing a mathematical model or function that can be used to predict or determine one variable by another variable is called regression analysis.

Question 14

Determine the equation of the trend line to forecast outcomes for time periods in the future,using alternative coding for time periods if necessary.

Question 15

The slope of the regression line,y = 21 − 5x,is 5.

Question 16

Explain what regression analysis is and the concepts of independent and dependent variable.

Question 17

Use the t and F tests to test hypotheses for both the slope of the regression model and the overall regression model.

Question 18

Calculate the coefficient of determination to measure the fit for regression models,and relate it to the coefficient of correlation.

Question 19

The difference between the actual y value and the predicted y value found using a regression equation is called the residual.

Question 20

The first step in simple regression analysis usually is to construct a scatter plot.

Question 21

The F value to test the overall significance of a regression model is computed by dividing the sum of squares regression (SS_reg)by the sum of squares error (SS_err).

Question 22

In the regression equation,y = 75.65 + 0.50x,the slope is ___.

A)0.50
B)75.65
C)1.00
D)0.00
E)-0.50

Question 23

From the following scatter plot,we can say that between y and x there is ___.

A)perfect positive correlation
B)virtually no correlation
C)positive correlation
D)negative correlation
E)perfect negative correlation

Question 24

In the regression equation,y = 75.65 + 0.50x,the intercept is ___.

A)0.50
B)75.65
C)1.00
D)0.00
E)-0.50

Question 25

The range of admissible values for the coefficient determination is −1 to +1.

Question 26

A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a linear function of batch size (the number of boards produced in one lot or batch).The slope of the accountant's model is ___.

A)batch size
B)unit variable cost
C)fixed cost
D)total cost
E)total variable cost

Question 27

A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a function of batch size (the number of boards produced in one lot or batch).The explanatory variable is ___.

A)batch size
B)unit variable cost
C)fixed cost
D)total cost
E)total variable cost

Question 28

A t test is used to determine whether the coefficients of the regression model are significantly different from zero.

Question 29

The coefficient of determination is the proportion of variability of the dependent variable (y)accounted for or explained by the independent variable (x).

Question 30

A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a function of batch size (the number of boards produced in one lot or batch).The dependent variable is ___.

A)batch size
B)unit variable cost
C)fixed cost
D)total cost
E)total variable cost

Question 31

The proportion of variability of the dependent variable (y)accounted for or explained by the independent variable (x)is called the coefficient of correlation.

Question 32

From the following scatter plot,we can say that between y and x there is ___.

A)perfect positive correlation
B)virtually no correlation
C)positive correlation
D)negative correlation
E)perfect negative correlation

Question 33

To determine whether the overall regression model is significant,the F test is used.

Question 34

In the simple regression model,y = 21 − 5x,if the coefficient of determination is 0.81,we can say that the coefficient of correlation between y and x is 0.90.

Question 35

A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a linear function of batch size (the number of boards produced in one lot or batch).The intercept of this model is the ___.

A)batch size
B)unit variable cost
C)fixed cost
D)total cost
E)total variable cost

Question 36

From the following scatter plot,we can say that between y and x there is ___.

A)perfect positive correlation
B)virtually no correlation
C)positive correlation
D)negative correlation
E)perfect negative correlation

Question 37

The numerical value of the coefficient of correlation must be ___.

A)between -1 and +1
B)between -1 and 0
C)between 0 and 1
D)equal to SSE/(n - 2)
E)between 0 and -1

Question 38

One of the major uses of residual analysis is to test some of the assumptions underlying regression.

Question 39

The following data is to be used to construct a regression model: The value of the y intercept is ___.

A)1.36
B)2.16
C)0.68
D)0.57
E)2.36

Question 40

In a simple regression the coefficient of correlation is the square root of the coefficient of determination.

Question 41

The following data is to be used to construct a regression model: The value of the slope is ___.

A)2.36
B)2.16
C)0.68
D)0.57
E)1.37

Question 42

The coefficient of correlation in a simple regression analysis is = - 0.6.The coefficient of determination for this regression would be ___.

A)0.6
B)- 0.6 or + 0.6
C)0.13
D)- 0.36
E)0.36

Question 43

A standard deviation of the error of the regression model is called the ___.

A)coefficient of determination
B)sum of squares of error
C)standard error of the estimate
D)R-squared
E)coefficient of correlation

Question 44

One of the assumptions made in simple regression is that ___.

A)the error terms are exponentially distributed
B)the error terms have unequal variances
C)the model is linear
D)the error terms are dependent
E)the model is nonlinear

Question 45

The assumptions underlying simple regression analysis include ___.

A)the error terms are exponentially distributed
B)the error terms have unequal variances
C)the model is nonlinear
D)the error terms are dependent
E)the error terms are independent

Question 46

For a certain data set the regression equation is y = 2 + 3x.The correlation coefficient between y and x in this data set ___.

A)must be 0
B)is negative
C)must be 1
D)is positive
E)must be 3

Question 47

For following scatter plot and regression line,at x = 65 the residual is ___.

A)positive
B)zero
C)negative
D)imaginary
E)unknown

Question 48

The assumption of constant error variance in regression analysis is called ___.

A)heteroscedasticity
B)homoscedasticity
C)residuals
D)linearity
E)non-normality

Question 49

One of the assumptions made in simple regression is that ___.

A)the error terms are normally distributed
B)the error terms have unequal variances
C)the model is nonlinear
D)the error terms are dependent
E)the error terms are all equal

Question 50

In regression analysis,R-squared is also called the ___.

A)residual
B)coefficient of determination
C)coefficient of correlation
D)standard error of the estimate
E)sum of squares of regression

Question 51

If x and y in a regression model are totally unrelated,___.

A)the correlation coefficient would be -1
B)the coefficient of determination would be 0
C)the coefficient of determination would be 1
D)the SSE would be 0
E)the MSE would be 0s

Question 52

The total of the squared residuals is called the ___.

A)coefficient of determination
B)sum of squares of error
C)standard error of the estimate
D)R-squared
E)coefficient of correlation

Question 53

The numerical value of the coefficient of determination must be ___.

A)between -1 and +1
B)between -1 and 0
C)between 0 and 1
D)equal to SSE/(n - 2)
E)between -100 and +100

Question 54

A simple regression model developed for ten pairs of data resulted in a sum of squares of error,SSE = 125.The standard error of the estimate is ___.

A)12.5
B)3.5
C)15.6
D)3.95
E)25

Question 55

The following residuals plot indicates ___.

A)a nonlinear relation
B)a nonconstant error variance
C)the simple regression assumptions are met
D)the sample is biased
E)a random sample

Question 56

The following data is to be used to construct a regression model: The regression equation is ___.

A)y = 2.16 + 1.37x
B)y = 1.37 + 2.16x
C)y = 0.69 + 0.57x
D)y = 0.57 + 0.69x
E)y = 0.57 - 0.69x

Question 57

For a certain data set the regression equation is y = 21 - 3x.The correlation coefficient between y and x in this data set ___.

A)must be 0
B)is negative
C)must be 1
D)is positive
E)must be >1

Question 58

Consider the following scatter plot and regression line.At x = 17,the residual (error term)is ___.

A)positive
B)zero
C)negative
D)imaginary
E)unknown

Question 59

The following residuals plot indicates ___.

A)a nonlinear relation
B)a nonconstant error variance
C)the simple regression assumptions are met
D)the sample is biased
E)the sample is random

Question 60

The proportion of variability of the dependent variable accounted for or explained by the independent variable is called the ___.

A)sum of squares error
B)coefficient of correlation
C)coefficient of determination
D)covariance
E)regression sum of squares

Question 61

A manager wants to predict the cost (y)of travel for salespeople based on the number of days (x)spent on each sales trip.The following model has been developed: y = $400 + 120x.If a trip took 3 days,the predicted cost of the trip is ___.

A)760
B)360
C)523
D)1560
E)1080

Question 62

Louis Katz,a cost accountant at Papalote Plastics,Inc.(PPI),is analyzing the manufacturing costs of a moulded plastic telephone handset produced by PPI.Louis's independent variable is production lot size (in 1,000's of units),and his dependent variable is the total cost of the lot (in $100's).Regression analysis of the data yielded the following tables: Using  = 0.05,Louis should ___.

A)increase the sample size
B)suspend judgment
C)not reject H₀: ₁ = 0
D)reject H₀: ₁ = 0
E)do not reject H₀: ₀ = 0

Question 63

Louis Katz,a cost accountant at Papalote Plastics,Inc.(PPI),is analyzing the manufacturing costs of a moulded plastic telephone handset produced by PPI.Louis's independent variable is production lot size (in 1,000's of units),and his dependent variable is the total cost of the lot (in $100's).Regression analysis of the data yielded the following tables: The correlation coefficient between Louis's variables is ___.

A)-0.73
B)0.73
C)0.28
D)-0.28
E)0.00

Question 64

In a regression analysis if SST = 200 and SSR = 200,r² = ___.

A)0.25
B)0.75
C)0.00
D)1.00
E)-1.00

Question 65

A manager wishes to predict the annual cost (y)of an automobile based on the number of kilometres (x)driven.The following model was developed: y = 1,550 + 0.36x.If a car is driven 15,000 kilometres,the predicted cost is ___.

A)2090
B)3850
C)7400
D)6950
E)5400

Question 66

Abby Kratz,a market specialist at the market research firm of Saez,Sikes,and Spitz,is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. 11ea888b_4160_b5c5_bb89_19f45c45177f_TB1680_00 For a household with $50,000 annual income,Abby's model predicts monthly grocery expenditures of ___.

A)$150.35
B)$50.35
C)$1,959.29
D)$128.65
E)$1286.50

s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. For a household with $50,000 annual income,Abby's model predicts monthly grocery expenditures of ___. A)$150.35 B)$50.35 C)$1,959.29 D)$128.65 E)$1286.50 " class="answers-bank-image d-block" loading="lazy" > For a household with $50,000 annual income,Abby's model predicts monthly grocery expenditures of ___.

A)$150.35
B)$50.35
C)$1,959.29
D)$128.65
E)$1286.50

s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. For a household with $50,000 annual income,Abby's model predicts monthly grocery expenditures of ___. A)$150.35 B)$50.35 C)$1,959.29 D)$128.65 E)$1286.50 " class="answers-bank-image d-block" loading="lazy" > 11ea888b_4160_b5c5_bb89_19f45c45177f_TB1680_00 For a household with $50,000 annual income,Abby's model predicts monthly grocery expenditures of ___.

A)$150.35
B)$50.35
C)$1,959.29
D)$128.65
E)$1286.50

Question 67

Louis Katz,a cost accountant at Papalote Plastics,Inc.(PPI),is analyzing the manufacturing costs of a moulded plastic telephone handset produced by PPI.Louis's independent variable is production lot size (in 1,000's of units),and his dependent variable is the total cost of the lot (in $100's).Regression analysis of the data yielded the following tables: Louis's sample size (n)is ___.

A)13
B)14
C)12
D)24
E)1

Question 68

A manager wishes to predict the annual cost (y)of an automobile based on the number of kilometres (x)driven.The following model was developed: y = 1,550 + .36x.If a car is driven 20,000 kilometres,the predicted cost is ___.

A)7,200
B)5,650
C)8,750
D)2,270
E)6,750

Question 69

Louis Katz,a cost accountant at Papalote Plastics,Inc.(PPI),is analyzing the manufacturing costs of a moulded plastic telephone handset produced by PPI.Louis's independent variable is production lot size (in 1,000's of units),and his dependent variable is the total cost of the lot (in $100's).Regression analysis of the data yielded the following tables: Louis's regression model is ___.

A)y = -0.358 + 3.996x
B)y = 0.358 + 3.996x
C)y = -3.996 + 0.358x
D)y = 3.996 - 0.358x
E)y = 3.996 + 0.358x

Question 70

Abby Kratz,a market specialist at the market research firm of Saez,Sikes,and Spitz,is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: 11ea888b_4160_197f_bb89_73f394b66705_TB1680_00 The correlation coefficient between the two variables in this regression is ___.

A)0.682478
B)-0.83
C)0.83
D)-0.68
E)1.0008

s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: The correlation coefficient between the two variables in this regression is ___. A)0.682478 B)-0.83 C)0.83 D)-0.68 E)1.0008 " class="answers-bank-image d-block" loading="lazy" > The correlation coefficient between the two variables in this regression is ___.

A)0.682478
B)-0.83
C)0.83
D)-0.68
E)1.0008

s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: The correlation coefficient between the two variables in this regression is ___. A)0.682478 B)-0.83 C)0.83 D)-0.68 E)1.0008 " class="answers-bank-image d-block" loading="lazy" > 11ea888b_4160_197f_bb89_73f394b66705_TB1680_00 The correlation coefficient between the two variables in this regression is ___.

A)0.682478
B)-0.83
C)0.83
D)-0.68
E)1.0008

Question 71

Abby Kratz,a market specialist at the market research firm of Saez,Sikes,and Spitz,is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables.  = 0.05,Abby should ___.

A)reject H₀: ₁ = 0
B)not reject H₀: ₁ = 0
C)increase the sample size
D)suspend judgment
E)reject H₀: ₀ = 0

s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. Using  = 0.05,Abby should ___. A)reject H₀: ₁ = 0 B)not reject H₀: ₁ = 0 C)increase the sample size D)suspend judgment E)reject H₀: ₀ = 0 " class="answers-bank-image d-block" loading="lazy" > 11ea888b_4160_8eb3_bb89_6b10bc08a163_TB1680_00 Using  = 0.05,Abby should ___.

A)reject H₀: ₁ = 0
B)not reject H₀: ₁ = 0
C)increase the sample size
D)suspend judgment
E)reject H₀: ₀ = 0

s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. Using  = 0.05,Abby should ___. A)reject H₀: ₁ = 0 B)not reject H₀: ₁ = 0 C)increase the sample size D)suspend judgment E)reject H₀: ₀ = 0 " class="answers-bank-image d-block" loading="lazy" > Using  = 0.05,Abby should ___.

A)reject H₀: ₁ = 0
B)not reject H₀: ₁ = 0
C)increase the sample size
D)suspend judgment
E)reject H₀: ₀ = 0

s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. Using  = 0.05,Abby should ___. A)reject H₀: ₁ = 0 B)not reject H₀: ₁ = 0 C)increase the sample size D)suspend judgment E)reject H₀: ₀ = 0 " class="answers-bank-image d-block" loading="lazy" > 11ea888b_4160_8eb3_bb89_6b10bc08a163_TB1680_00 Using  = 0.05,Abby should ___.

A)reject H₀: ₁ = 0
B)not reject H₀: ₁ = 0
C)increase the sample size
D)suspend judgment
E)reject H₀: ₀ = 0

Question 72

A researcher has developed a regression model from fourteen pairs of data points.He wants to test to determine if the slope is significantly different from zero.He uses a two-tailed test and  = 0.01.The critical table t value is ___.

A)2.650
B)3.012
C)3.055
D)2.718
E)2.168

Question 73

A manager wishes to predict the annual cost (y)of an automobile based on the number of kilometres (x)driven.The following model was developed: y = 1,550 + 0.36x.If a car is driven 30,000 kilometres,the predicted cost is ___.

A)10,800
B)12,350
C)2,630
D)9,250
E)10,250

Question 74

Louis Katz,a cost accountant at Papalote Plastics,Inc.(PPI),is analyzing the manufacturing costs of a moulded plastic telephone handset produced by PPI.Louis's independent variable is production lot size (in 1,000's of units),and his dependent variable is the total cost of the lot (in $100's).Regression analysis of the data yielded the following tables: For a lot size of 10,000 handsets,Louis' model predicts total cost will be ___.

A)$4,031.80
B)$757.60
C)$3,960.20
D)$354.01
E)$1873.077

Question 75

A manager wants to predict the cost (y)of travel for salespeople based on the number of days (x)spent on each sales trip.The following model has been developed: y = $400 + 120x.If a trip took 4 days,the predicted cost of the trip is ___.

A)480
B)880
C)524
D)2080
E)1080

Question 76

Abby Kratz,a market specialist at the market research firm of Saez,Sikes,and Spitz,is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: 11ea888b_415f_cb5d_bb89_3f3309f7ca00_TB1680_00 Abby's regression model is ___.

A)y = 39.15 + 2.79x
B)y = 39.15 - 1.79x
C)y = 1.79 + 39.15x
D)y = -1.79 + 39.15x
E)y = 39.15 + 1.79x

s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: Abby's regression model is ___. A)y = 39.15 + 2.79x B)y = 39.15 - 1.79x C)y = 1.79 + 39.15x D)y = -1.79 + 39.15x E)y = 39.15 + 1.79x " class="answers-bank-image d-block" loading="lazy" > Abby's regression model is ___.

A)y = 39.15 + 2.79x
B)y = 39.15 - 1.79x
C)y = 1.79 + 39.15x
D)y = -1.79 + 39.15x
E)y = 39.15 + 1.79x

s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: Abby's regression model is ___. A)y = 39.15 + 2.79x B)y = 39.15 - 1.79x C)y = 1.79 + 39.15x D)y = -1.79 + 39.15x E)y = 39.15 + 1.79x " class="answers-bank-image d-block" loading="lazy" > 11ea888b_415f_cb5d_bb89_3f3309f7ca00_TB1680_00 Abby's regression model is ___.

A)y = 39.15 + 2.79x
B)y = 39.15 - 1.79x
C)y = 1.79 + 39.15x
D)y = -1.79 + 39.15x
E)y = 39.15 + 1.79x

Question 77

A researcher has developed a regression model from fifteen pairs of data points.He wants to test to determine if the slope is significantly different from zero.He uses a two-tailed test and  = 0.10.The critical table t value is ___.

A)1.771
B)1.350
C)1.761
D)2.145
E)2.068

Question 78

Abby Kratz,a market specialist at the market research firm of Saez,Sikes,and Spitz,is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: 11ea888b_4160_4091_bb89_cbaf4c9f23b1_TB1680_00 Abby's sample size (n)is ___.

A)8
B)10
C)11
D)20
E)12

s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: Abby's sample size (n)is ___. A)8 B)10 C)11 D)20 E)12 " class="answers-bank-image d-block" loading="lazy" > Abby's sample size (n)is ___.

A)8
B)10
C)11
D)20
E)12

s),and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: Abby's sample size (n)is ___. A)8 B)10 C)11 D)20 E)12 " class="answers-bank-image d-block" loading="lazy" > 11ea888b_4160_4091_bb89_cbaf4c9f23b1_TB1680_00 Abby's sample size (n)is ___.

A)8
B)10
C)11
D)20
E)12

Question 79

If there is perfect negative correlation between two sets of numbers,then ___.

A)r = 0
B)r = -1
C)r = +1
D)SSE=1
E)MSE = 1

Question 80

Alan Bissell,market analyst for City Sound Mart,is analyzing the relation between heavy metal CD sales and the size of the teenage population.He gathers data from six sales districts.Alan's dependent variable is annual heavy metal CD sales (in $1,000,000's),and his independent variable is teenage population (in 1,000's).Regression analysis of the data yielded the following tables: Alan's regression model can be written as: ___.

A)y = 7.950352 - 0.48455x
B)y = -0.48455 + 7.950352x
C)y = -0.14156 + 0.105195x
D)y = 0.105195 - 0.14156x
E)y = 0.105195 + 0.14156x